Metamaterials and Cesàro convergence

Abstract

In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence. Then, we also show that the analytical continuation of the linear permittivity \& permeability to a complex plane in terms of Riemann zeta function. The metamaterials are fabricated materials with a negative refractive index. These materials, in turn, depend on permittivity \& permeability of the linear dielectrics and magnetic materials. Therefore, the Cesàro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.

AIP Advances 2020

References in corpus (3)

• Achieving control of in-plane elastic waves
• The negative index of refraction demystified
• The refractive index and wave vector in passive or active media